Waiting at Rome Airport for Travel Partners

Am I able to wait in my airline lounge and go through Passport Control at the same time as my daughters do

Does your airline let you use the lounge AFTER the flight? I have been able to use a lounge only before or between flights, is why I ask.

Are you overnighting in Rome? Honestly, I'd take a taxi to the hotel and get out and walk some if your room isn't ready. It's a flat rate taxi fee from the airport in to Rome.

Same^^
Sitting around for 3 hours would be the worst for jet lag

Are your daughters adults?

I do not know Rome airport, but you have not had many responses so I am going to give you my thoughts as I fly into Europe usually twice a year.

Once you get off the aircraft you are expected to walk or shuttle straight to Passport control. You cannot hang out for three-plus hours waiting to go through passport control with your daughters. Security staff will not allow you to do this and there is no lounge area just walkways. Passport control may be backed up and you may need an hour here anyway. Keep in mind, It might take you 20 mins to get off the plane to walk to passport control depending on your seat on the aircraft.
You will then walk through customs with your carry-on luggage, then follow the exit signs (bypass baggage claim) until you arrive in the arrivals area where there is usually an information desk, ATMs, Train ticket office, etc. You can probably pick up coffee here. You could hang out here if need be. We did this one time in Zurich airport where one of us was 2 hours ahead. She waited in Starbucks for us. On the other hand, when I was ahead 8 hours on a trip to Greece this year, I went straight to the hotel with a pre-booked driver. Airport Lounges are usually only in the connections or departure lounges. You can't go into that area without having access or a boarding pass for that day.

Thank you ! This was great advice. I will enjoy some peace and quiet at the hotel.

Specific to FCO, there is an arrivals lounge, which has a nominal admission fee:

https://www.adr.it/web/aeroporti-di-roma-en/hellosky

Since you are landing at 7:45am, I would check with the hotel as to their
early check-in policy. Just because there is a room available does not
mean you will automatically be able to access it early. However, most
likely they will be happy to store your bags and maybe offer you a coffee
and a seat in the public area to relax. Or just go out and get to know the
neighborhood a bit.

In 2019, after an overnight flight I waited in the Hello Sky lounge for several hours to meet up with my sister and brother-in-law who were flying in from Germany. It was worth the 8 euro (I think) fee.

Thank you Shoeflyer for adding the specific details for Rome. I wanted to bump up her questions so just responded with general information.